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# If n and k are integers, is (−1)^(4n+k) less than 0?

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Director
Joined: 24 Oct 2016
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GMAT 1: 670 Q46 V36
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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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29 Mar 2019, 06:01
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82% (00:42) correct 18% (01:32) wrong based on 55 sessions

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If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q

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Re: If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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29 Mar 2019, 06:14
If n and k are integers, is (−1)^(4n+k) less than 0?

$$(−1)^{(4n+k)}=(-1)^{4n}*(-1)^k=((-1)^2)^{2n}+(-1)^1*(-1)^k$$
So we require to know the property of k.
If it is odd, $$(−1)^{(4n+k)}<0$$, and if k is even, $$(−1)^{(4n+k)}>0$$

(1) n is an even number
We require the property of k.

(2) k is an odd number
So, answer is YES for 'Is (−1)^(4n+k) less than 0?
Sufficient

B'
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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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Updated on: 29 Mar 2019, 08:17
1
dabaobao wrote:
If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q

C-Trap Q

Theory:

(-1)^even power = always +
(-1)^odd power = always -

Simplify the Q

4n is always even. So (-1)^4n would always be +
So we only care about (-1)^k. If we know the power of k, then we can tell whether (−1)^(4n+k) is <0 or >0.

Hence, simplified Q: Is k even or odd?

Solving the Simplified Q

1) Don't care about whether n is even or odd since 4n would always be even. Hence (−1)^(4n) would be even. Need k. Not sufficient.

2) K=odd. This is what we wanted sufficient.

Make sure to not fall in the C-Trap by thinking that you need both k and n. This is a common trap that GMAT likes to use on 700 level Qs.

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Originally posted by dabaobao on 29 Mar 2019, 06:19.
Last edited by dabaobao on 29 Mar 2019, 08:17, edited 1 time in total.
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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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29 Mar 2019, 06:50
First of all, rewrite the given number as: $$-1^{4n} * -1^k$$.
Statement 1: we don't know anything about $$k$$. If $$k$$ was even, the number would be positive; otherwise, if $$k$$ was odd, the number would be negative. Provided information is not sufficient.
Statement 2: $$k$$ is odd. Since $$4n = even * odd/even = even$$, what we derive is $$-1^{4n} = positive$$ and $$-1^k = negative$$. The whole number will be less than $$0$$. Sufficient. Hence, B.
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Re: If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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29 Mar 2019, 11:10
dabaobao wrote:
If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q

#1
value of k not know
#2
odd = k and 4n= even
so value <0
IMO B
Re: If n and k are integers, is (−1)^(4n+k) less than 0?   [#permalink] 29 Mar 2019, 11:10
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